supply chain location models

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Models For
Facility Location
And
Capacity Allocation

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Contents:-
1. Need
2. Types of Models
3. Network Optimization Model
4. Gravity Location Model
5. Allocation and location
6. References

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Total
Revenues
Product
Sale
Facilities
Labor
Transportation
Materials
Inventories
Profit + Taxes
Increasing Facilities and capacity
decreases transportation costs but
increases inventory costs.
1. Need:-
Aim is to design a network
which increases Profitability
with apt. Responsiveness.

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Phases in network design:-
Phase I Phase II Phase III Phase
IV
A. Network Optimization Model
B. Gravity Location Models
2. Types of Models:-

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3. Network Optimization Model.

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Steps:-

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Example:- Capacitated Plant location model
Capacities of plants are known.
n = Number of Potential Plant Locations
m = Number of markets or demand points
Dj = annual demand from market j
Ki = potential capacity of plant i
Fi = annualized fixed costs for keeping factory i open
Cij = cost of producing and shipping one unit from factory
i to market j

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Yi = 1 if plant i is open , else 0.
Xij = quantity shipped fron plant i to market j.
So,
Min ∑Fi*Yi + ∑∑ Cij*Xij
Subject to:
∑Xij = Dj For j= 1 to m
∑Xij ≤ Ki * Yi For i = 1 to n
Yi є {0,1} For i = 1 to n, Xij ≥ 0
n mn
i=1 i=1 j=1
m
j=1
n
i=1


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4. Gravity Location Model.

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Basic Model:
F1
S1
S2
S3
M2
M3
M1
(Xn,Yn) = Co ordinate location of either market or supply
source n
Fn = Cost of Shipping One unit for one mile between
facility and either market or supply source n
Dn = Quantity to be shipped between facility and either
market or supply source n

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Let,
(X,Y) = location selected for the facility
dn = distance between the facility at location (X,Y)
and Supply source or market n is given by:-
dn = √(X-Xn) + (Y-Yn)
The total Transportation cost TC:-
TC = ∑ (dn * Dn * Fn)
The optimal location is one that minimizes TC.
2 2
k
n=1

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5. Allocation And Location:-
a. Allocating Demand to production facilities:
Find Xij s
b. Locating Plants
Find Yi=1s
c. Locating Plants and Warehouses Simultaneously
Introducing new decision variables
Introducing new constraints
Introducing certain changes in the objective
function

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6. References:-
a. Supply Chain Management By Sunil Chopra ,
Third Edition.
b. citeseerx.ist.psu.edu
c. www.dms.umontreal.ca

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